Assuming these are three separate problems, I have solved them for you below.
1.) [tex]-x - y - 3z = -9[/tex]
[tex]⇒ -x + (-y + y) + (-3z + 3z) = -9 + 3z + y[/tex]
[tex]⇒ -x = -9 + 3z + y[/tex]
Multiply the whole thing by -1 so x is positive.
[tex]x = 9 - 3z - y[/tex]
2.) [tex]z = -3x - 1[/tex]
⇒ [tex]z + 1 = -3x + (-1 + 1)[/tex]
⇒ [tex]z + 1 = -3x[/tex]
Isolate x⇒ [tex]\frac{z + 1 = -3x}{-3}[/tex]
⇒[tex]\frac{1}{3}z + \frac{1}{3} = x[/tex]
3.) [tex]x - 5y + z = 21[/tex]
⇒ [tex](-x + x) + -5y + (z - z) = 21 - z - x[/tex]
⇒ [tex]\frac{-5y = 21 - z - x}{-5}[/tex]
⇒ [tex]y = \frac{1}{5}x + \frac{1}{5}z - \frac{21}{5}[/tex]
